Quantum circuits for performing arithmetic operations are an essential part of key quantum algorithms such as Shor's factorization, discrete logarithm, hidden subgroup algorithms and others. The importance of quantum ternary logic for applications such as quantum key distribution has been understood since late 1980s. Recently, ternary arithmetic has become important in quantum computing due to potential architectural platforms grounded in ternary representation, for example in the metaplectic any on architecture. Ternary quantum logic may also be relevant for other architectural platforms such as quantum dots, where higher energy levels can be used to store additional logic states. While ternary hardware architectures have been investigated, satisfactory circuits and procedures for ternary arithmetic and ternary quantum logic for algorithm and circuit compilation are generally unavailable.